Research On The Relation Between "CPFS Structure"and High School Students' Flexible And Profound Thingking In Mathematics And Experimental Research

Thinking has always been regarded as "the most beautiful human flower" , "Mathematics, known as the empress of science, is considered as the gymnastics of thinking. As stated in "The Mathematics Course Standard in High School" to be implemented nationwide soon, mathematics plays a unique and irreplaceable role in forming man' s reasoning ability in thinking and promoting people' s intelligence. Mathematics education empowers the students with the abilities to solve problems from the point of view of mathematics and in consequence get to know the world. " In the last few years, students' quality and potentials in mathematics have been more and more stressed in the national matriculation mathematics tests, believing that mathematics is an important media through which the reasoning ability is developed and the students thinking ability is trained and promoted by means of structural modes judgments, analysis, summary, deduction, inference , demonstration etc. Currently, the information age has posed a great challenge to people' s traditional modes of thinking and thinking with the help of the internet is a symbol of a new stage of people' s mode of thinking.A lot of achievements have been made in the research of the thinking ability in mathematics both at home and abroad, the research remains superficial, lacking experiments upon which to base the research. Besides, little research has been made of the thinking ability in advanced mathematics has long been a problem. When talking about "the key issues concerning the research in mathematics education and its trend and teacher development of mathematics teachers, Zheng Yu-xin pointed out "emphasis should be laid on the actual thinking activity the students are involved in in the course of learning of mathematics instead of on the analysis of the teaching material and the research of methodology. As far as the teaching of mathematics is concerned, teaching the basic knowledge of mathematics and the knowledge concerning teaching is not enough, we should also take into account the students' cognitive quality. Based on the above mentioned, I have selected from the CPFS Structure,— which is considered unique cognitive structure of mathematics, and high school students' thinking in mathematics,—two important indexes of thinking, i. e. flexibility and profoundness as the focus of my research., trying to study the relation between each individual' s psychological "CPFS Structure" and the flexibility and profoundness in high school students' thinking quality and its effect from a totally new perspective.Based on the questionnaire and case study, this paper analyzes the current situation and problems in high school students' thinking in mathematics and their cognitive structure andtraces the cause of these problems. On the basis if these, it then further carries on research on the relation between the "CPFS Structure" and the flexibility and profoundness in high school students' ability of thinking in mathematics and discusses the teaching strategy on how to improve each individual' s psychological CPFS Structure in learning mathematics in the classroom., for example, introducing the strategy of creating barriers in the course of a lesson to stimulate the students to think, problem chains to improve the teacher' s teaching strategy and assigning homework of different levels to students of mixed abilities and making a chart of the subject to be learned to improve the students' learning strategy. In addition, I have also introduced Polya' s Problem Solving Table and the training of strategy in problem solving in my research to promote the students' initial cognitive experience and monitoring strategy. To sum up, after a year' s experiment and research, based on both qualitative and quantitative analysis, I have come to the conclusion that the CPFS Structure is a good one promoting the students' learning of mathematics, that the perfection of the CPFS Structure can effectively improve the students' flexibility and profoundness in thinking in mathematics, and at the same time promote such non-intellectual qualities as their interest in mathematics, motivation and attitude and as a result improve their performance in learning mathematics and their research ability in mathematics.